Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A
We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X). We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem. T...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/216035 |
| Summary: | We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X). We prove that the equation has a unique positive definite solution via
variable replacement and fixed point theorem. The basic fixed point iteration for the equation is given. |
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| ISSN: | 1085-3375 1687-0409 |